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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 57, 2008 - Issue 4
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Original Articles

A scaled nonlinear conjugate gradient algorithm for unconstrained optimization

Pages 549-570 | Received 29 May 2005, Accepted 19 Jul 2006, Published online: 23 May 2008

References

  • Andrei , N . 2004 . A new gradient descent method for unconstrained optimization , ICI Technical Report . March
  • Barzilai , J and Borwein , JM . 1998 . Two point step size gradient method . IMA Journal Numers Analysis , 8 : 141 – 148 .
  • Birgin , E and Martínez , JM . 2001 . A spectral conjugate gradient method for unconstrained optimization . Applied Mathematics and Optimization , 43 : 117 – 128 .
  • Bongartz , I , Conn , AR , Gould , NIM and Toint , PL . 1995 . CUTE: constrained and unconstrained testing environments . ACM Transactions on Mathematical Software , 21 : 123 – 160 .
  • Cauchy , A . 1847 . Méthodes générales pour la résolution des systèmes déquations simultanées . C.R. de l'Académie des Sciences , 25 : 536 – 538 . Paris
  • Dai , YH and Liao , LZ . 2001 . New conjugate conditions and related nonlinear conjugate gradient methods . Applied Mathematics and Optimization , 43 : 87 – 101 .
  • Dai , YH and Yuan , JY . 1998 . Convergence properties of the Beale–Powell restart algorithm . Sciences in China (Series A) , 41 ( 11 ) : 1142 – 1150 .
  • Dai , YH , Yuan , JY and Yuan , Y . 2002 . Modified two-point stepsize gradient methods for unconstrained optimization . Computational Optimization and Applications , 22 : 103 – 109 .
  • Dolan , ED and Moré , JJ . 2002 . Benchmarking optimization software with performance profiles . Mathematical Programming , 91 : 201 – 213 .
  • Fletcher , R . 2005 . “ On the Barzilai–Borwein method ” . In Optimization and Control Applications Edited by: Qi , L , Teo , K and Yang , X . 235 – 256 . Series: Applied Optimization, Vol. 96, Springer, Berlin
  • Fletcher , R and Reeves , CM . 1964 . Function minimization by conjugate gradients . Computer Journal , 7 : 149 – 154 .
  • Hager , WW and Zhang , H . 2005 . A new conjugate gradient method with guaranteed descent and an efficient line search . SIAM Journal of Optimization , 16 : 170 – 192 .
  • Hestenes , MR and Stiefel , E . 1952 . Methods of conjugate gradients for solving linear systems . Journal Research of the National Bureau of Standards Section B , 48 : 409 – 436 .
  • Oren , SS . 1974 . Self–scaling variable metric algorithm. Part II . Management Science , 20 : 863 – 874 .
  • Oren , SS and Luenberger , DG . 1976 . Self-scaling variable metric algorithm. Part I . Management Science , 20 : 845 – 862 .
  • Oren , SS and Spedicato , E . 1976 . Optimal conditioning of self-scaling variable metric algorithms . Mathematical Programming , 10 : 70 – 90 .
  • Perry , JM . 1977 . A class of conjugate gradient algorithms with a two step variable metric memory , Northwestern University . Discussion Paper 269, Center for Mathematical Studies in Economics and Management Science
  • Polak , E and Ribière , G . 1969 . Note sur la convergence de méthodes de directions conjuguées . Revue Francaise Informat. Reserche Opérationnelle , 16 : 35 – 43 .
  • Powell , MJD . 1977 . Restart procedures for the conjugate gradient method . Mathematical Programming , 12 : 241 – 254 .
  • Raydan , M . 1997 . The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem . SIAM Journal of Optimization , 7 : 26 – 33 .
  • Shanno , DF . 1978 . Conjugate gradient methods with inexact searches . Mathematics of Operations Research , 3 : 244 – 256 .
  • Shanno , DF . 1978 . On the convergence of a new conjugate gradient algorithm . SIAM Journal Numers Analysis , 15 : 1247 – 1257 .
  • Shanno , DF and Phua , KH . 1976 . Algorithm 500, minimization of unconstrained multivariate functions . ACM Transactions on Mathematical Software , 2 : 87 – 94 .
  • Wolfe , P . 1969 . Convergence conditions for ascent methods . SIAM Reviews , 11 : 226 – 235 .
  • Wolfe , P . 1971 . Convergence conditions for ascent methods II: some corrections . SIAM Reviews , 13 : 185 – 188 .

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